We present a technique to directly excite Luttinger liquid collective modes in carbon nanotubes at GHz frequencies. We are embarking on a set of experiments to measure the dynamical conductivity of an individual SWNT at microwave (GHz) frequencies. The goal is to measure the conductivity as a function of frequency for frequencies above and below the scattering frequency. The contact can be either ohmic, or capacitive. A further goal is the direct electrical excitation of the 1d plasmon, which is the low-energy excitation of a Luttinger liquid, as well as measuring the plasmon wave velocity and damping.

By modeling the nanotube as a nano-transmission line with distributed kinetic and magnetic inductance as well as distributed quantum and electrostatic capacitance, we calculate the complex, frequency dependent impedance for a variety of measurement geometries. Exciting voltage waves on the nano-transmission line is equivalent to directly exciting the yet-to-be observed one dimensional plasmons, the low energy excitation of a Luttinger liquid. Our technique has already been applied to 2d plasmons and should work well for 1d plasmons. Ohmic contact is not necessary with our technique; capacitive contacts can work.

We will measure 1d plasmons by applying the same experimental technique we recently developed to measure 2d plasmons at microwave frequencies (P.J. Burke, http://xxx.lanl.gov/abs/cond-mat/0204262; Burke, et al, Appl. Phys. Lett., 76 (6), 745-747 (2000); Burke, et al, 'Interlayer Plasmons', available at http://nano.ece.uci.edu). The technique consists of measuring resonant behavior in the frequency dependent microwave impedance (real and imaginary parts) which corresponds to standing waves of the 1d plasmon in the finite length tube. The experiments will have to overcome several technical challenges: 1) High quality SWNTs must be grown with lengths of order 10-100 microns. 2) These must be coupled to a well-quantified microwave measurements setup. 3) The microwave electronics must be able to measure high-impedance devices.

Finally, our work has direct bearing on asking the question: What is fT for a nanotube based field effect transistor? In contrast to high-electron mobility transistors, the kinetic inductance contributes an additional (distributed) circuit element in the high frequency transistor equivalent circuit model which must be included to answer the question: What is the speed limit of molecular electronics?